There are many other examples where the score-type statistics are adopted for change point analysis,
including those based on likelihood ratio or classical \(M\) -estimators [1]}
and those for testing for changes in linear (auto)regression [2]}, [3]},
integer-valued time series such as Poisson autoregressive processes [4]}
and even regression models based on neural networks [5]}.
In all of the above, the test statistics are based on partial sums
\(\frac{1}{\sqrt{n}} \max _{1 \le k < n} \left\Vert  \sum _{t = 1}^k F(\mathbf {Y}_t, \widehat{\beta }_{0:n}) \right\Vert \quad \text{where} \quad \sum _{t = 1}^n F(\mathbf {Y}_t, \widehat{\beta }_{0:n}) = 0,\) 
